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Beliebt Rechnen >

integral of (x-3)^2sin(x-3)

Lösung

\int (x - 3)^{2} sin (x - 3) d x

Lösung

- x^{2} cos (x - 3) + 6 x cos (x - 3) + 2 x sin (x - 3) - 7 cos (x - 3) - 6 sin (x - 3) + C

Schritte zur Lösung

\int (x - 3)^{2} sin (x - 3) d x

Wende U-Substitution an

= \int u^{2} sin (u) d u

Wende die partielle Integration an

= - u^{2} cos (u) - \int - 2 u cos (u) d u

\int - 2 u cos (u) d u = - 2 (u sin (u) + cos (u))

= - u^{2} cos (u) - (- 2 (u sin (u) + cos (u)))

Setze in

u = x - 3

ein

= - (x - 3)^{2} cos (x - 3) - (- 2 ((x - 3) sin (x - 3) + cos (x - 3)))

Vereinfache

- (x - 3)^{2} cos (x - 3) - (- 2 ((x - 3) sin (x - 3) + cos (x - 3))) : - x^{2} cos (x - 3) + 6 x cos (x - 3) + 2 x sin (x - 3) - 7 cos (x - 3) - 6 sin (x - 3)

= - x^{2} cos (x - 3) + 6 x cos (x - 3) + 2 x sin (x - 3) - 7 cos (x - 3) - 6 sin (x - 3)

Füge eine Konstante zur Lösung hinzu

= - x^{2} cos (x - 3) + 6 x cos (x - 3) + 2 x sin (x - 3) - 7 cos (x - 3) - 6 sin (x - 3) + C

Graph

Beliebte Beispiele

integral of 8tan(8x)

\int 8 tan (8 x) d x

limit as x approaches 9 of sqrt(25-x)

x \to 9 lim (25 - x)

tangent f(x)=3x^2-10x

t an g e n t f (x) = 3 x^{2} - 10 x

derivative pix^3

d er i v a t i v e π x^{3}

derivative y=e^{2x}tan(2x)

d er i v a t i v e y = e^{2 x} tan (2 x)